Wormhole solutions in a generalized hybrid metric-Palatini matter theory, given by a gravitational Lagrangian f(R,R), where R is the metric Ricci scalar, and R is a Palatini scalar curvature defined ...in terms of an independent connection, and a matter Lagrangian, are found. The solutions are worked in the scalar-tensor representation of the theory, where the Palatini field is traded for two scalars, φ and ψ, and the gravitational term R is maintained. The main interest in the solutions found is that the matter field obeys the null energy condition (NEC) everywhere, including the throat and up to infinity, so that there is no need for exotic matter. The wormhole geometry with its flaring out at the throat is supported by the higher-order curvature terms, or equivalently, by the two fundamental scalar fields, which either way can be interpreted as a gravitational fluid. Thus, in this theory, in building a wormhole, it is possible to exchange the exoticity of matter by the exoticity of the gravitational sector. The specific wormhole displayed, built to obey the matter NEC from the throat to infinity, has three regions, namely, an interior region containing the throat, a thin shell of matter, and a vacuum Schwarzschild anti-de Sitter (AdS) exterior. For hybrid metric-Palatini matter theories this wormhole solution is the first where the NEC for the matter is verified for the entire spacetime keeping the solution under asymptotic control. The existence of this type of solutions is in line with the idea that traversable wormholes bore by additional fundamental gravitational fields, here disguised as scalar fields, can be found without exotic matter. Concomitantly, the somewhat concocted architecture needed to assemble a complete wormhole solution for the whole spacetime may imply that in this class of theories such solutions are scarce.
We study the thermodynamics of a five-dimensional Schwarzschild black hole, also known as a five-dimensional Schwarzschild-Tangherlini black hole, in the canonical ensemble using York's formalism. ...Inside a cavity of fixed size r and fixed temperature T, we find that there is a threshold at πrT = 1 above which a black hole can be in thermal equilibrium with the cavity's boundary. Moreover, this thermal equilibrium can only be achieved for two specific types of black holes. One is a small black hole (compared with the cavity size r) of horizon radius r+1 , while the other is a large black hole (of the order of the cavity size r) of horizon radius r+2 . In five dimensions, the radii r+1 and r+2 have an exact expression. Through the path integral formalism, which directly yields the partition function of the system, one obtains the action and thus the free energy for the black hole in the canonical ensemble. The procedure leads naturally to the thermal energy and entropy of the canonical system, the latter turning out to be given by the Bekenstein-Hawking area law S = A+/4, where the black hole's surface area in five dimensions is A + = 2π2r3+ and r+ stands for both r+1 and r+2. We also calculate the heat capacity and find that it is positive when the heat bath is placed at a radius r that is equal or less than the photonic orbit, implying in this case thermodynamic stability, and instability otherwise. This means that the small black hole r+1 is unstable and the large one r+2 is stable. A generalized free energy is used to compare the possible thermodynamic phase transitions relative to classical hot flat space which has zero free energy, and we show that it is feasible in certain instances that classical hot flat space transits through r+1 to settle at the stable r+2, with the free energy of the unstable smaller black hole r+1 acting as the potential barrier between the two states. It is also shown that, remarkably, the free energy of the larger r+2 black hole is zero when the cavity radius is equal to the Buchdahl radius. The relation to the instabilities that arise due to perturbations in the path integral in the instanton solution is mentioned. Hot flat space is made of gravitons and it should be treated quantum mechanically rather than classically. Quantum hot flat space has negative free energy and we find the conditions for which the large black hole phase, quantum hot flat space phase, or both are the ground state of the canonical ensemble. The corresponding phase diagram is displayed in a r × T plot showing clearly the three possible phases. Using the density of states ν at a given energy E we also find that the entropy of the large black hole r+2 is S = A+2/4. In addition, we make the connection between the five-dimensional thermodynamics and York's four-dimensional results.
We study the thermodynamics of a d-dimensional Schwarzschild black hole, also known as a Schwarzschild-Tangherlini black hole, in the canonical ensemble. This generalizes York's formalism, which has ...been initially applied to four dimensions and later to five dimensions, to any number d of dimensions. The canonical ensemble, characterized by a cavity of fixed radius r and fixed temperature T at the boundary, allows for two possible black hole solutions in thermal equilibrium, a smaller black hole and a larger black hole. In four and five dimensions, these solutions have a direct exact form, whereas in an arbitrary number of dimensions, one is compelled to resort to approximation schemes or numerical calculations. From the Euclidean action and the path integral approach, we obtain the free energy, the thermodynamic energy, the thermodynamic pressure, and the entropy, of the black hole plus cavity system. The entropy of the system is given by the Bekenstein-Hawking area law. The analysis of the heat capacity of the system shows that the smaller black hole is in unstable equilibrium and the larger black hole is in stable equilibrium. The d-dimensional photon sphere radius divides the stability criterion. Indeed, if the cavity's radius is larger than the photon sphere radius, and so the black hole is small, the system is unstable, if the cavity's radius is smaller than the photon sphere radius, and so the black hole is large, the system is stable. To study perturbations on the system, a generalized free energy function is obtained that also allows one to understand the possible phase transitions between classical hot flat space and the black holes. The Buchdahl radius, that appears naturally in the general relativistic study of star structure, also shows up in our context; the free energy is zero when the cavity's radius has the d-dimensional Buchdahl radius value. Then, if the cavity's radius is larger than the Buchdahl radius, classical hot flat space phase cannot make a phase transition to a black hole phase, and if smaller, classical hot flat space can nucleate a black hole. The roles of both the photon sphere and the Buchdahl limit are present for every dimension d, indicating that, besides their known role in dynamics, these radii also play a role in the thermodynamics of gravitational systems. The close link between the canonical analysis performed and the direct perturbation of the path integral is also pointed out. Since hot flat space is a quantum system made purely of gravitons, if only gravitation is considered, it is of great interest to compare the d-dimensional free energies of quantum hot flat space and the stable black hole to find for which ranges of r and T, the quantities that characterize the canonical ensemble, one phase predominates over the other. Phase diagrams for a few different dimensions are displayed. The density of states at a given energy is found through an inverse Laplace transformation giving back the entropy of the stable black hole. Several side calculations and further deliberations are performed, namely, the calculation for the approximate expressions for the canonical ensemble black hole horizon radii, a brief study of the photon orbit radius and the Buchdahl radius in the d-dimensional Schwarzschild solution, a connection to the thermodynamics of thin shells in d spacetime dimensions which are systems that are also apt to a rigorous thermodynamic study, a presentation of quantum hot flat space in d spacetime dimensions as a thermodynamic system, an analysis of classical hot flat space in d spacetime dimensions as a product of quantum hot flat space with the black hole transitions and the corresponding phase diagrams for a few different dimensions, and a synopsis with the relevance of the work. It is still worth mentioning that the comparison of the thermodynamics of d-dimensional Schwarzschild black holes and classical hot flat space in the canonical ensemble with the thermodynamics of spherical thin shells in d dimensions yields a striking direct matching between the two systems, most notably that the photon sphere radius appears here as a thermodynamic stability divisor in both systems, and the Buchdahl radius that appears on thermodynamic grounds for canonical black holes appears also as a thermodynamic and as a dynamical radius for thin shells.
We consider new regular exact spherically symmetric solutions of a nonminimal Einstein-Yang-Mills theory with a cosmological constant and a gauge field of magnetic Wu-Yang type. The most interesting ...solutions found are black holes with metric and curvature invariants that are regular everywhere, i.e., regular black holes. We set up a classification of the solutions according to the number and type of horizons. The structure of these regular black holes is characterized by four specific features: a small cavity in the neighborhood of the center, a repulsion barrier off the small cavity, a distant equilibrium point, in which the metric function has a minimum, and a region of Newtonian attraction. Depending on the sign and value of the cosmological constant, the solutions are asymptotically de Sitter (dS), asymptotically flat, or asymptotically anti-de Sitter (AdS).
We classify all fundamental electrically charged thin shells in general relativity, i.e., static spherically symmetric perfect fluid thin shells with a Minkowski spacetime interior and a ...Reissner-Nordström spacetime exterior, characterized by the spacetime mass M , which we assume positive, and the electric charge Q , which without loss of generality in our analysis can always be assumed as being the modulus of the electric charge, be it positive or negative. The fundamental shell can exist in three states, namely, nonextremal when Q/M < 1 , which includes the Schwarzschild Q/M = 0 state, extremal when Q/M = 1 , and overcharged when Q/M > 1 . The nonextremal state, Q M < 1 , allows the shell to be located in such a way that the radius R of the shell can be outside its own gravitational radius r+ , i.e., R > r+ , where r+ is given in terms of M and Q by ..., or can be inside its own Cauchy radius r−, i.e., R < r−, where r − is given in terms of M and Q by ... . The extremal state, Q/M = 1 , allows the shell to be located in such a way that the radius R of the shell can be outside its own gravitational radius r+ , i.e., R > r+, where now r+ = r−, or can be inside its own gravitational radius, i.e., R < r + , or can be at its own gravitational radius r+, i.e., R = r+. The overcharged state, Q M > 1 , allows the shell to be located anywhere R ≥ 0 . There is yet a further division; indeed, one has still to specify the orientation of the shell, i.e., whether the normal out of the shell points toward increasing radii or toward decreasing radii. For the shell's orientation, the analysis in the nonextremal state is readily performed using Kruskal-Szekeres coordinates, whereas in the extremal and overcharged states the analysis can be performed in the usual spherical coordinates. There is still a subdivision in the extremal state r+ = r− when the shell is at r+, R = r+, in that the shell can approach r + from above or approach r + from below. The shell is assumed to be composed of an electrically charged perfect fluid characterized by the energy density, pressure, and electric charge density, for which an analysis of the energy conditions, null, weak, dominant, and strong, is performed. In addition, the shell spacetime has a corresponding Carter-Penrose diagram that can be built out of the diagrams for Minkowski and Reissner-Nordström spacetimes. Combining these two characterizations, specifically, the physical properties and the Carter-Penrose diagrams, one finds that there are fourteen cases that comprise a bewildering variety of shell spacetimes, namely, nonextremal star shells, nonextremal tension shell black holes, nonextremal tension shell regular and nonregular black holes, nonextremal compact shell naked singularities, Majumdar-Papapetrou star shells, extremal tension shell singularities, extremal tension shell regular and nonregular black holes, Majumdar-Papapetrou compact shell naked singularities, Majumdar-Papapetrou shell quasiblack holes, extremal null shell quasinonblack holes, extremal null shell singularities, Majumdar-Papapetrou null shell singularities, overcharged star shells, and overcharged compact shell naked singularities. (ProQuest: ... denotes formulae omitted.)
Using a dynamical system approach we study the cosmological phase space of the generalized hybrid metric-Palatini gravity theory, characterized by the function f ( R , R ) , where R is the metric ...scalar curvature and R the Palatini scalar curvature of the spacetime. We formulate the propagation equations of the suitable dimensionless variables that describe FLRW universes as an autonomous system. The fixed points are obtained for four different forms of the function f ( R , R ) , and the behavior of the cosmic scale factor a ( t ) is computed. We show that due to the structure of the system, no global attractors can be present and also that two different classes of solutions for the scale factor a ( t ) exist. Numerical integrations of the dynamical system equations are performed with initial conditions consistent with the observations of the cosmological parameters of the present state of the Universe. In addition, using a redefinition of the dynamic variables, we are able to compute interesting solutions for static universes.
Cosmology of f ( R , ❑ R ) gravity Carloni, Sante; Rosa, João Luís; Lemos, José P. S.
Physical review. D,
05/2019, Letnik:
99, Številka:
10
Journal Article
Recenzirano
Using dynamical system analysis, we explore the cosmology of theories of order up to eighth order of the form f(R,❑R). The phase space of these cosmologies reveals that higher-order terms can have a ...dramatic influence on the evolution of the cosmology, avoiding the onset of finite time singularities. We also confirm and extend some of results which were obtained in the past for this class of theories.
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