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Register a new userArea bound for surfaces in generic gravitational field
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We define an attractive gravity probe surface (AGPS) as a compact 2-surface $S_alpha$ with positive mean curvature $k$ satisfying $r^a D_a k / k^2 ge alpha$ (for a constant $alpha>-1/2$) in the local inverse mean curvature flow, where $r^a D_a k$ is the derivative of $k$ in the outward unit normal direction. For asymptotically flat spaces, any AGPS is proved to satisfy the areal inequality $A_alpha le 4pi [ ( 3+4alpha)/(1+2alpha) ]^2(Gm)^2$, where $A_{alpha}$ is the area of $S_alpha$ and $m$ is the Arnowitt-Deser-Misner (ADM) mass. Equality is realized when the space is isometric to the $t=$constant hypersurface of the Schwarzschild spacetime and $S_alpha$ is an $r=mathrm{constant}$ surface with $r^a D_a k / k^2 = alpha$. We adapt the two methods of the inverse mean curvature flow and the conformal flow. Therefore, our result is applicable to the case where $S_alpha$ has multiple components. For anti-de Sitter (AdS) spaces, a similar inequality is derived, but the proof is performed only by using the inverse mean curvature flow. We also discuss the cases with asymptotically locally AdS spaces.
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We study the polarizations of gravitational waves (GWs) in two classes of extended gravity theories. First, we formulate the polarizations in linear massive gravity (MG) with generic mass terms of non-Fierz-Pauli type by identifying all the independent variables that obey Klein-Gordon-type equations. The dynamical degrees of freedom (dofs) in the generic MG consist of spin-2 and spin-0 modes, the former breaking down into two tensor (helicity-2), two vector (helicity-1) and one scalar (helicity-0) components, while the latter just corresponding to a scalar. We find convenient ways of decomposing the two scalar modes of each spin into distinct linear combinations of the transverse and longitudinal polarizations with coefficients directly expressed by the mass parameters, thereby serving as a useful tool in measuring the masses of GWs. Then we analyze the linear perturbations of generic higher-curvature gravity (HCG) whose Lagrangian is an arbitrary polynomial of the Riemann tensor. On a flat background, the linear dynamical dofs in this theory are identified as massless spin-2, massive spin-2, and massive spin-0 modes. As its massive part encompasses the identical structure to the generic MG, GWs in the generic HCG provide six massive polarizations on top of the ordinary two massless modes. In parallel to MG, we find convenient representations for the scalar-polarization modes directly connected to the parameters of HCG. In this analysis, we employ two distinct methods; One takes full advantage of the partial equivalence between the generic HCG and MG at the linear level, whereas the other relies upon a gauge-invariant formalism. We confirm that the two results agree. We also discuss methods to determine the theory parameters by GW-polarization measurements. Our method does not require measuring the propagation speeds or the details of the waveforms of the GWs. [Abridged]
We propose a new concept, the transversely trapping surface (TTS), as an extension of the static photon surface characterizing the strong gravity region of a static/stationary spacetime in terms of photon behavior. The TTS is defined as a static/stationary timelike surface $S$ whose spatial section is a closed two-surface, such that arbitrary photons emitted tangentially to $S$ from arbitrary points on $S$ propagate on or toward the inside of $S$. We study the properties of TTSs for static spacetimes and axisymmetric stationary spacetimes. In particular, the area $A_0$ of a TTS is proved to be bounded as $A_0le 4pi(3GM)^2$ under certain conditions, where $G$ is the Newton constant and $M$ is the total mass. The connection between the TTS and the loosely trapped surface proposed by us [arXiv:1701.00564] is also examined.
We study the gravitational radiation emitted during the scattering of two spinless bodies in the post-Minkowskian Effective Field Theory approach. We derive the conserved stress-energy tensor linearly coupled to gravity and the classical probability amplitude of graviton emission at leading and next-to-leading order in the Newtons constant $G$. The amplitude can be expressed in compact form as one-dimensional integrals over a Feynman parameter involving Bessel functions. We use it to recover the leading-order radiated angular momentum expression. Upon expanding it in the relative velocity between the two bodies $v$, we compute the total four-momentum radiated into gravitational waves at leading-order in $G$ and up to an order $v^8$, finding agreement with what was recently computed using scattering amplitude methods. Our results also allow us to investigate the zero frequency limit of the emitted energy spectrum.
In this paper we analyze the gravitational field of a global monopole in the context of $f(R)$ gravity. More precisely, we show that the field equations obtained are expressed in terms of $F(R)=frac{df(R)}{dR}$. Since we are dealing with a spherically symmetric system, we assume that $F(R)$ is a function of the radial coordinate only. Moreover, adopting the weak field approximation, we can provide all components of the metric tensor. A comparison with the corresponding results obtained in General Relativity and in the Brans-Dicke theory is also made.
The main aim of this paper is twofold. (1) Exact solutions of a scalar field in the Schwarzschild spacetime are presented. The exact wave functions of scattering states and bound-states are presented. Besides the exact solution, we also provide explicit approximate expressions for bound-state eigenvalues and scattering phase shifts. (2) By virtue of the exact solutions, we give a direct calculation for the discontinuous jump on the horizon for massive scalar fields, while in literature such a jump is obtained from an asymptotic solution by an analytic extension treatment.
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