In this work we derive the junction conditions for the matching between two spacetimes at a separation hypersurface in the perfect-fluid version of f( R, T ) gravity, not only in the usual ...geometrical representation but also in a dynamically equivalent scalar-tensor representation. We start with the general case in which a thin shell separates the two spacetimes at the separation hypersurface, for which the general junction conditions are deduced, and the particular case for smooth matching is considered when the stress-energy tensor of the thin shell vanishes. The set of junction conditions is similar to the one previously obtained for f(R) gravity but features also constraints in the continuity of the trace of the stress-energy tensor Tab and its partial derivatives, which force the thin shell to satisfy the equation of state of radiation σ = 2 pt. As a consequence, a necessary and sufficient condition for spherically symmetric thin shells to satisfy all the energy conditions is the positivity of its energy density σ . For specific forms of the function f ( R , T ) , the continuity of R and T ceases to be mandatory but a gravitational double layer arises at the separation hypersurface. The Martinez thin-shell system and a thin shell surrounding a central black hole are provided as examples of application.
Cosmological sudden singularities in f(R, T) gravity Gonçalves, Tiago B.; Rosa, João Luís; Lobo, Francisco S. N.
The European physical journal. C, Particles and fields,
05/2022, Letnik:
82, Številka:
5
Journal Article
Recenzirano
Odprti dostop
In this work, we study the possibility of finite-time future cosmological singularities appearing in
f
(
R
,
T
) gravity, where
R
is the Ricci scalar and
T
is the trace of the stress-energy tensor. ...We present the theory in both the geometrical and the dynamically equivalent scalar–tensor representation and obtain the respective equations of motion. In a background Friedmann–Lemaître–Robertson–Walker (FLRW) universe with an arbitrary curvature and for a generic
C
∞
function
f
(
R
,
T
), we prove that the conservation of the stress-energy tensor prevents the appearance of sudden singularities in the cosmological context at any order in the time-derivatives of the scale factor. However, if this assumption is dropped, the theory allows for sudden singularities to appear at the level of the third time-derivative of the scale factor
a
(
t
), which are compensated by divergences in either the first time-derivatives of the energy density
ρ
(
t
)
or the isotropic pressure
p
(
t
). For these cases, we introduce a cosmological model featuring a sudden singularity that is consistent with the current measurements for the cosmological parameters, namely, the Hubble constant, deceleration parameter, and age of the universe, and provide predictions for the still unmeasured jerk and snap parameters. Finally, we analyse the constraints on a particular model of the function
f
(
R
,
T
) that guarantees that the system evolves in a direction favorable to the energy conditions at the divergence time.
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