Related papers: On Effective Potential in Tortoise Coordinate
Scale dependence at the level of the effective action is a generic result of quantum field theory. Allowing for scale dependence of the gravitational couplings leads to a generalization of the corresponding field equations. In this work,…
In this paper a Banados, Teitelboim and Zanelli (BTZ) black hole is constructed from an exact solution of the Einstein field equations in a (2+1)-dimensional anti-de Sitter spacetime in the context of noncommutative geometry. The BTZ black…
The functional Schrodinger equation is used to study the quantum collapse of a gravitating, spherical domain wall and a massless scalar field coupled to the metric. The approach includes backreaction of pre-Hawking radiation on the…
This paper is devoted to the study of the existence of positive and bounded solutions for a Schr\"odinger type equation defined on the entire Euclidean space, involving a general integro-differential operator. We consider the case where the…
It has been suggested in the literature that, given a black hole spacetime, a relativistic membrane can provide an effective description of the horizon dynamics. In this paper, we explore such a framework in the context of a 2+1-dimensional…
We investigate the quantum dynamics of a charged scalar field in the near-horizon region of a near-extremal charged BTZ black hole. A controlled expansion of the Einstein-Maxwell equations reveals an emergent warped AdS$_2 \times S^1$…
We investigate static and spherically symmetric solutions in a gravity theory that extends the standard Hilbert-Einstein action with a Lagrangian constructed from a three-form field $A_{\alpha \beta \gamma}$, which is related to the field…
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…
We study the massive scalar field equation $\Box_g \phi = m^2 \phi$ on a stationary and spherically symmetric black hole $g$ (including in particular the Schwarzschild and Reissner--Nordstr\"om black holes in the full sub-extremal range)…
We show that the method used in the Schwarzschild black hole for finding the elementary solution of the electrostatic equation in closed form cannot extend in higher dimensions. By contrast, we prove the existence of static, spherically…
We study classical scalar fields in asymptotically Lifshitz spacetimes. By evading Derrick's theorem requiring the scalar potential to explicitly depend on the background coordinates, we induce a diffeomorphism invariance breaking and…
We investigate the properties of the Schwarzschild black hole geometry involving leading one-loop long-distance quantum effects, which arise within the framework of effective field theories of gravity. Our analysis reveals that geodesic…
We investigate thermodynamic behaviors of the $D$-dimensional gravity coupled to a dynamical unit timelike vector, the aether, present two kinds of exact charged solutions and study the linearized wave spectrum of this theory. There is an…
We introduce a two-parameter static, nonspherically-symmetric black hole solution in the Einstein theory of gravity coupled with a massless scalar field. The scalar field depends only on the polar coordinate $\theta$ in the spherical…
We study the structure and stability of spherically symmetric Brans-Dicke black-hole type solutions with an infinite horizon area and zero Hawking temperature, existing for negative values of the coupling constant $\omega$. These solutions…
We consider motion of a particle in the background of a stationary axially symmetric generic black hole. A particle experiences the action of a force of unspecified nature. We require the force to remain finite in a comoving frame. The…
Pseudo-Newtonian gravitational potential describing the gravitational field of static and spherically symmetric black holes in the universe with a repulsive cosmological constant is introduced. In order to demonstrate the accuracy of the…
The asymptotic behavior of solutions to Schr\"odinger equations with singular homogeneous potentials is investigated. Through an Almgren type monotonicity formula and separation of variables, we describe the exact asymptotics near the…
We obtain approximate analytical solutions of the Einstein equations close to the trapping horizon for a dynamical spherically symmetric black hole in the presence of a minimally coupled self-interacting scalar field. This is made possible…
A class of harmonic solutions to the steady Euler equations for incompressible fluids is presented in two dimensions in circular, elliptic and bipolar coordinates. Since the velocity field is solenoidal in this case, it can be written as…