Generalized Rastall’s gravity and its effects on compact objects. (arXiv:2007.01968v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Mota_C/0/1/0/all/0/1">Clésio E. Mota</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Santos_L/0/1/0/all/0/1">Luis C. N. Santos</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Silva_F/0/1/0/all/0/1">Franciele M. da Silva</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Grams_G/0/1/0/all/0/1">Guilherme Grams</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Lobo_I/0/1/0/all/0/1">Iarley P. Lobo</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Menezes_D/0/1/0/all/0/1">Débora P. Menezes</a>
We present a generalization of Rastall’s gravity in which the conservation
law of the energy-moment tensor is altered, and as a result, the trace of the
energy-moment tensor is taken into account together with the Ricci scalar in
the expression for the covariant derivative. Afterwards, we obtain the field
equation in this theory and solve it by considering a spherically symmetric
space-time. We show that the external solution has two possible classes of
solutions with spherical symmetry in the vacuum in generalized Rastall’s
gravity. The first class of solutions is completely equivalent to the
Schwarzschild solution, while the second class of solutions has the same
structure as the Schwarzschild–de Sitter solution in general relativity. The
generalization, in contrast to constant value $k=8pi G$ in general relativity,
has a gravitational parameter $k$ that depends on the energy density $rho$. As
an application, we perform a careful analysis of the effects of the theory on
neutron stars using realistic equations of state (EoS) as inputs. Our results
show that important differences on the profile of neutron stars are obtained
within two representatives EoS.
We present a generalization of Rastall’s gravity in which the conservation
law of the energy-moment tensor is altered, and as a result, the trace of the
energy-moment tensor is taken into account together with the Ricci scalar in
the expression for the covariant derivative. Afterwards, we obtain the field
equation in this theory and solve it by considering a spherically symmetric
space-time. We show that the external solution has two possible classes of
solutions with spherical symmetry in the vacuum in generalized Rastall’s
gravity. The first class of solutions is completely equivalent to the
Schwarzschild solution, while the second class of solutions has the same
structure as the Schwarzschild–de Sitter solution in general relativity. The
generalization, in contrast to constant value $k=8pi G$ in general relativity,
has a gravitational parameter $k$ that depends on the energy density $rho$. As
an application, we perform a careful analysis of the effects of the theory on
neutron stars using realistic equations of state (EoS) as inputs. Our results
show that important differences on the profile of neutron stars are obtained
within two representatives EoS.
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