Near-zone symmetries of Kerr black holes Hui, Lam; Joyce, Austin; Penco, Riccardo ...
The journal of high energy physics,
09/2022, Letnik:
2022, Številka:
9
Journal Article
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A
bstract
We study the near-zone symmetries of a massless scalar field on four-dimensional black hole backgrounds. We provide a geometric understanding that unifies various recently discovered ...symmetries as part of an SO(4
,
2) group. Of these, a subset are exact symmetries of the static sector and give rise to the ladder symmetries responsible for the vanishing of Love numbers. In the Kerr case, we compare different near-zone approximations in the literature, and focus on the implementation that retains the symmetries of the static limit. We also describe the relation to spin-1 and 2 perturbations.
Abstract
We derive the quadratic action for the physical degrees of freedom of massless spin-0, spin-1, and spin-2 perturbations on a Schwarzschild-(A)dS background in arbitrary dimensions. We then ...use these results to compute the static response of asymptotically flat Schwarzschild black holes to external fields. Our analysis reproduces known facts about black hole Love numbers — in particular that they vanish for all types of perturbation in four spacetime dimensions — but also leads to new results. For instance, we find that neutral Schwarzschild black holes polarize in the presence of an electromagnetic background in any number of spacetime dimensions except four. Moreover, we calculate for the first time black hole Love numbers for vector-type gravitational perturbations in higher dimensions and find that they generically do not vanish. Along the way, we shed some light on an apparent discrepancy between previous results in the literature, and clarify some aspects of the matching between perturbative calculations of static response on a Schwarzschild background and the point-particle effective theory.
Abstract
It is well known that asymptotically flat black holes in general
relativity have a vanishing static, conservative tidal response. We show that this is a result of linearly realized ...symmetries governing
static (spin 0,1,2)
perturbations around black holes. The symmetries have a geometric origin: in the scalar case, they arise from the (E)AdS isometries of a dimensionally reduced black hole spacetime. Underlying the symmetries is a ladder structure which can be used to construct the full tower of solutions,
and derive their general properties: (1) solutions that decay with
radius spontaneously break the symmetries, and must
diverge at the horizon;
(2) solutions regular at the horizon respect the symmetries, and
take the form of a finite polynomial that grows with radius.
Taken together, these two properties imply that static response coefficients — and in particular Love numbers — vanish. Moreover, property (1) is consistent with the absence of black holes with linear (perturbative) hair. We also discuss the manifestation of these symmetries in the effective point particle description of a black hole, showing explicitly that for scalar probes
the worldline couplings associated with a non-trivial tidal response and scalar hair must vanish in order for the symmetries to be preserved.
We explore the duality invariance of the Maxwell and linearized Einstein–Hilbert actions on a non-rotating black hole background. On-shell, these symmetries are electric–magnetic duality and ...Chandrasekhar duality, respectively. Off-shell, they lead to conserved quantities; we demonstrate that one of the consequences of these conservation laws is that even- and odd-parity metric perturbations have equal Love numbers. Along the way, we derive an action principle for the Fackerell–Ipser equation and Teukolsky–Starobinsky identities in electromagnetism.
Lorentz-violating theories of gravity typically contain constrained vector fields. We show that the lowest-order coupling of such vectors to U(1)-symmetric scalars can naturally give rise to ...baryogenesis in a manner akin to the Affleck–Dine mechanism. We calculate the cosmology of this new mechanism, demonstrating that a net B−L can be generated in the early Universe, and that the resulting baryon-to-photon ratio matches that which is presently observed. We discuss constraints on the model using solar system and astrophysical tests of Lorentz violation in the gravity sector. Generic Lorentz-violating theories can give rise to the observed matter–antimatter asymmetry without violating any current bounds.
We argue that dark energy with multiple fields is theoretically well-motivated and predicts distinct observational signatures, in particular when cosmic acceleration takes place along a trajectory ...that is highly non-geodesic in field space. Such models provide novel physics compared to ΛCDM and quintessence by allowing cosmic acceleration on steep potentials. From the theoretical point of view, these theories can easily satisfy the conjectured swampland constraints and may in certain cases be technically natural, potential problems which are endemic to standard single-field dark energy. Observationally, we argue that while such multi-field models are likely to be largely indistinguishable from the concordance cosmology at the background level, dark energy perturbations can cluster, leading to an enhanced growth of large-scale structure that may be testable as early as the next generation of cosmological surveys.
We consider how the swampland criteria might be applied to models in which scalar fields have nontrivial kinetic terms, particularly in the context of P(φ,X) theories, popularly used in approaches to ...inflation, to its alternatives, and to the problem of late-time cosmic acceleration. By embedding such theories in canonical multi-field models, from which the original theory emerges as a low-energy effective field theory, we derive swampland constraints, and study the circumstances under which these might be evaded while preserving cosmologically interesting phenomenology. We further demonstrate how these successes are tied to the phenomenon of turning in field space in the multi-field picture. We study both the general problem and specific examples of particular interest, such as DBI inflation.
Bimetric theory describes gravitational interactions in the presence of an extra spin-2 field. Previous work has suggested that its cosmological solutions are generically plagued by instabilities. We ...show that by taking the Planck mass for the second metric, Mf, to be small, these instabilities can be pushed back to unobservably early times. In this limit, the theory approaches general relativity with an effective cosmological constant which is, remarkably, determined by the spin-2 interaction scale. This provides a late-time expansion history which is extremely close to ΛCDM, but with a technically-natural value for the cosmological constant. We find Mf should be no larger than the electroweak scale in order for cosmological perturbations to be stable by big-bang nucleosynthesis. We further show that in this limit the helicity-0 mode is no longer strongly-coupled at low energy scales.
Massive mimetic cosmology Solomon, Adam R.; Vardanyan, Valeri; Akrami, Yashar
Physics letters. B,
07/2019, Letnik:
794, Številka:
C
Journal Article
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We study the first cosmological implications of the mimetic theory of massive gravity recently proposed by Chamseddine and Mukhanov. This is a novel theory of ghost-free massive gravity which ...additionally contains a mimetic dark matter component. In an echo of other modified gravity theories, there are self-accelerating solutions which contain a ghost instability. In the ghost-free region of parameter space, the effect of the graviton mass on the cosmic expansion history amounts to an effective negative cosmological constant, a radiation component, and a negative curvature term. This allows us to place constraints on the model parameters—the graviton mass and the Stückelberg vacuum expectation value—by insisting that the effective radiation and curvature terms be within observational bounds. The late-time acceleration must be accounted for by a separate positive cosmological constant or other dark energy sector. We impose further constraints at the level of perturbations by demanding linear stability. We comment on the possibility of distinguishing this theory from ΛCDM with current and future large-scale structure surveys.
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