Case Of Einstein Gravity Research Articles

Non-extremal near-horizon geometries

When Gaussian null coordinates are adapted to a Killing horizon, the near-horizon limit is defined by a coordinate rescaling and then by taking the regulator parameter ɛ to be small, as a way of zooming into the horizon hypersurface. In this coordinate setting, it is known that the metric of a non-extremal Killing horizon in the near-horizon limit is divergent, and it has been a common practice to impose extremality in order to set the divergent term to zero. Although the metric is divergent, we show for a class of Killing horizons that the vacuum Einstein’s equations can be separated into a divergent and a finite part, leading to a well-defined minimal set of Einstein’s equations one needs to solve. We extend the result to Einstein gravity minimally coupled to a massless scalar field. We also discuss the case of Einstein gravity coupled to a Maxwell field, in which case the separability holds if the Maxwell potential has non-vanishing components only in the directions of the horizon spatial cross section.

Inflationary model in minimally modified gravity theories

We have investigated inflationary model constructed from minimally modified gravity (MMG) theories. The MMG theory in the form of $f({\bf H}) \propto {\bf H}^{1+p}$ gravity where, ${\bf H}$ is the Hamiltonian constraint in the Einstein gravity and $p$ is constant, has been studied. An inflation is difficult to be achieved in this theory of gravity unless an additional scalar field playing a role of inflaton is introduced in the model. We have found that the inflaton with exponential potential can drive inflation with graceful exist different from the case of Einstein gravity. The slow-roll parameter for both the exponential and the power-law potentials is inversely proportional to number of e-folding similar to the case of the Einstein gravity. We also have found for the scalar perturbation that the curvature perturbation in the comoving gauge on super Hubble radius scales grows rapidly during inflation unless $p =0$. For the tensor modes, the amplitude of the perturbations is constant on large scales, and sound speed of the perturbations can diviate from unity and can vary with time depending on the form of $f({\bf H})$.

Slowly rotating black holes in Einsteinian cubic gravity

We construct slowly rotating black-hole solutions of Einsteinian cubic gravity (ECG) in four dimensions with flat and AdS asymptotes. At leading order in the rotation parameter, the only modification with respect to the static case is the appearance of a non-vanishing $g_{t\phi}$ component. Similarly to the static case, the order of the equation determining such component can be reduced twice, giving rise to a second-order differential equation which can be easily solved numerically as a function of the ECG coupling. We study how various physical properties of the solutions are modified with respect to the Einstein gravity case, including its angular velocity, photon sphere, photon rings, shadow, and innermost stable circular orbits (in the case of timelike geodesics).

Quasinormal modes and spectroscopy of a Schwarzschild black hole surrounded by a cloud of strings in Rastall gravity

We obtain the solution of a static spherically symmetric black hole surrounded by a cloud of strings in Rastall gravity and study the influence of the parameter $a$ associated with strings on the event horizon and the Hawking temperature. Through analyzing the black hole metric, we find that the static spherically symmetric black hole solution surrounded by a cloud of strings in Rastall gravity can be transformed into the static spherically symmetric black hole solution surrounded by quintessence in Einstein gravity when the parameter $\beta$ of Rastall gravity is positive, which provides a possibility for the string fluid to be a candidate of dark energy. We use the method of Regge and Wheeler together with the high order WKB-Pad\'{e} approximation to calculate the quasinormal mode frequencies of the odd parity gravitational perturbation and simultaneously apply the unstable null geodesics of black holes to compute the quasinormal mode frequencies at the eikonal limit for this black hole model. The results show that the increase of the parameter $a$ makes the gravitational wave decay slowly in Rastall gravity. In addition, we utilize two methods, which are based on the adiabatic invariant integral and the periodic property of outgoing waves, respectively, to derive the area spectrum and entropy spectrum of the black hole model. The results show that the area spectrum and entropy spectrum are equidistant spaced. The former is same as the case of Einstein gravity, while the latter is different, depending on the Rastall parameter $\beta$.

Reconstruction of general relativistic cosmological solutions in modified gravity theories

We study the special class of the exact solutions in cosmological models based on the Generalized Scalar-Tensor Gravity with non-minimal coupling of a scalar field to the Ricci scalar and to the Gauss-Bonnet scalar in 4D Friedmann universe corresponding to similar ones in GR. The parameters of cosmological perturbations in such models correspond to the case of Einstein gravity with a high precision. As the example of proposed approach, we obtain the exact solutions for the power-law and exponential power-law inflation.

Quasinormal Modes of the Schwarzschild Black Hole Surrounded by the Quintessence Field in Rastall Gravity**Supported by the National Nature Science Foundation of Education Department of Shannxi Province under Grant No. 15JK1077 and the Doctorial Scientific Research Starting Fund of Shannxi University of Science and Technology under Grant No. BJ12-02

The quasinormal modes of the Schwarzschild black hole surrounded by the quintessence in Rastall gravity are studied using the sixth-order Wentzel-Kramers-Brillouin approximative approach. The effect of the Rastall parameter on the quasinormal modes of gravitational, electromagnetic and massless scalar perturbations is explored. Compared to the case of Einstein gravity, it is found that, when , the gravitational field, electromagnetic field as well as massless scalar field damp more rapidly and have larger real frequency of oscillation in Rastall gravity, while when , the gravitational field, electromagnetic field as well as massless scalar field damp more slowly and have smaller real frequency of oscillation in Rastall gravity. It is also found that the gravitational field, electromagnetic field as well as massless scalar field damp more and more slowly and the real frequency of oscillation for the gravitational perturbation, electromagnetic perturbation as well as massless scalar perturbation becomes smaller and smaller as the Rastall parameter η increases. Compared among the quasinormal frequencies of gravitational, electromagnetic and massless scalar perturbations, I find that, for fixed η, (l,n), ϵ and Nq, the oscillation damps most slowly for the gravitational perturbation, mediate for the electromagnetic perturbation and most rapidly for the massless scalar perturbation, and the real frequency of oscillation is the smallest for the gravitational perturbation, mediate for the electromagnetic perturbation and the largest for the massless scalar perturbation in Rastall gravity.

Towards the Cardy formula for hyperscaling violation black holes

The aim of this paper is to propose a generalized Cardy formula in the case of three-dimensional hyperscaling violation black holes. We first note that for the hyperscaling violation metrics, the scaling of the entropy in term of the temperature (defined as the effective spatial dimensionality divided by the dynamical exponent) depends explicitly on the gravity theory. Starting from this observation, we first explore the case of quadratic curvature gravity theory for which we derive four classes of asymptotically hyperscaling violation black holes. For each solution, we compute their masses as well as those of their soliton counterparts obtained through a double Wick rotation. Assuming that the partition function has a certain invariance involving the effective spatial dimensionality, a generalized Cardy formula is derived. This latter is shown to correctly reproduce the entropy where the ground state is identified with the soliton. Comparing our formula with the one derived in the standard Einstein gravity case with source, we stress the role played by the effective spatial dimensionality. From this observation, we speculate the general form of the Cardy formula in the case of hyperscaling violation metric for an arbitrary value of the effective spatial dimensionality. Finally, we test the viability of this formula in the case of cubic gravity theory.

AdS/BCFT correspondence for higher curvature gravity: an example

We consider the effects of higher curvature terms on a holographic dual description of boundary conformal field theory. Specifically, we consider three-dimensional gravity with a specific combination of Ricci tensor square and curvature scalar square, so called, new massive gravity. We show that a boundary entropy and an entanglement entropy are given by similar expression with those of the Einstein gravity case when we introduce an {\it effective} Newton's constant and an {\it effective} cosmological constant. We also show that the holographic g-theorem still holds in this extension, and we give some comments about the central charge dependence of boundary entropy in the holographic construction. In the same way, we consider new type black holes and comment on the boundary profile. Moreover, we reproduce these results through auxiliary field formalism in this specific higher curvature gravity.

The black hole membrane paradigm in f(R) gravity

To an outside observer, a black hole’s event horizon appears to behave exactly like a dynamical fluid membrane. We extend this membrane paradigm to black holes in general f(R) theories of gravity. We derive the stress tensor and various transport coefficients of the fluid and find that the membrane behaves as a non-Newtonian fluid except for the special case of Einstein gravity. Using Euclidean methods, we study the thermodynamics of the membrane. We speculate on what theories of gravity admit horizons with fluid properties.

C-functions in Lovelock gravity

We present C-functions for static and spherically symmetric spacetimes in Lovelock gravity theories. These functions are monotonically increasing functions of the outward radial coordinate and acquire their minima when evaluated on the horizon. Unlike the case of Einstein gravity, where there is a single C-function, we find that this function is non-unique in the case of Lovelock gravity. We define two C-functions, which agree at the horizon giving the black hole entropy, and state the different energy conditions that must hold in order for these functions to satisfy the monotonicity condition.

Bound monopoles in Brans–Dicke theory

We consider axially symmetric SU(2) Yang–Mills–Higgs (YMH) multimonopoles in Brans–Dicke theory for winding number n>1. In analogy to the spherically symmetric n=1 solutions, we find that the axially symmetric solutions exist for higher values of the gravitational coupling than in the pure Einstein gravity case. For large values of the gravitational coupling, the solutions collapse to form a black hole which outside the horizon can be described by an extremal Reissner–Nordström solution. Similarly as in the pure Einstein gravity case, like-charged monopoles reside in an attractive phase in a limited domain of parameter space. However, we find that the strength of attraction is decreasing for decreasing Brans–Dicke parameter ω.

Inflaton potential reconstruction in the braneworld scenario

We consider inflaton potential reconstruction in the context of the simplest braneworld scenario, where both the Friedmann equation and the form of scalar and tensor perturbations are modified at high energies. We derive the reconstruction equations, and analyze them analytically in the high-energy limit and numerically for the general case. As previously shown by Huey and Lidsey, the consistency equation between scalar and tensor perturbations is unchanged in the braneworld scenario. We show that this leads to a perfect degeneracy in reconstruction, whereby a different viable potential can be obtained for any value of the brane tension $\ensuremath{\lambda}.$ Accordingly, the initial perturbations alone cannot be used to distinguish the braneworld scenario from the usual Einstein gravity case.

Monopole inflation in Brans-Dicke theory

According to previous work, topological defects expand exponentially without end if the vacuum expectation value of the Higgs field is of the order of the Planck mass. We extend the study of inflating topological defects to Brans-Dicke gravity. With the help of numerical simulations we investigate the dynamics and spacetime structure of a global monopole. Contrary to the case of Einstein gravity, any inflating monopole eventually shrinks and takes a stable configuration. We also discuss cosmological constraints on the model parameters.