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Register a new userVacuum decay and quadratic gravity: the massive case
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False vacuum decay in field theory may be formulated as a boundary value problem in Euclidean space. In a previous work, we studied its solution in single scalar field theories with quadratic gravity and used it to find obstructions to vacuum decay. For simplicity, we focused on massless scalar fields and false vacua with a flat geometry. In this paper, we generalize those findings to massive scalar fields with the same gravitational interactions, namely an Einstein-Hilbert term, a quadratic Ricci scalar, and a non-minimal coupling. We find that the scalar field reaches its asymptotic value faster than in the massless case, in principle allowing for a wider range of theories that may accommodate vacuum decay. Nonetheless, this hardly affects the viability of the bounce in the scenarios here considered. We also briefly consider other physically interesting theories by including higher-order kinetic terms and changing the number of spacetime dimensions.
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Metastable states decay at zero temperature through quantum tunneling at an exponentially small rate, which depends on the Coleman-de Luccia instanton, also known as bounce. In some theories, the bounce may not exist or its on-shell action may be ill-defined or infinite, thus hindering the vacuum decay process. In this paper, we test this possibility in modified theories of gravity interacting with a real scalar field. We consider an Einstein-Hilbert term with a non-minimally coupled scalar field and a quadratic Ricci scalar contribution. To tackle the problem we use a new analytic method, with which we prove that the scalar field on the bounce has a universal behavior at large Euclidean radii, almost independently of the potential. Our main result is that the quadratic Ricci scalar prevents the decay, regardless of the other terms in the action. We also comment on the numerical implications of our findings.
We study static, spherically symmetric vacuum solutions to Quadratic Gravity, extending considerably our previous Rapid Communication [Phys. Rev. D 98, 021502(R) (2018)] on this topic. Using a conformal-to-Kundt metric ansatz, we arrive at a much simpler form of the field equations in comparison with their expression in the standard spherically symmetric coordinates. We present details of the derivation of this compact form of two ordinary differential field equations for two metric functions. Next, we apply analytical methods and express their solutions as infinite power series expansions. We systematically derive all possible cases admitted by such an ansatz, arriving at six main classes of solutions, and provide recurrent formulas for all the series coefficients. These results allow us to identify the classes containing the Schwarzschild black hole as a special case. It turns out that one class contains only the Schwarzschild black hole, three classes admit the Schwarzschild solution as a special subcase, and two classes are not compatible with the Schwarzschild solution at all since they have strictly nonzero Bach tensor. In our analysis, we naturally focus on the classes containing the Schwarzschild spacetime, in particular on a new family of the Schwarzschild-Bach black holes which possesses one additional non-Schwarzschild parameter corresponding to the value of the Bach tensor invariant on the horizon. We study its geometrical and physical properties, such as basic thermodynamical quantities and tidal effects on free test particles induced by the presence of the Bach tensor. We also compare our results with previous findings in the literature obtained using the standard spherically symmetric coordinates.
We consider a finite-size spherical bubble with a nonequilibrium value of the $q$-field, where the bubble is immersed in an infinite vacuum with the constant equilibrium value $q_{0}$ for the $q$-field (this $q_{0}$ has already cancelled an initial cosmological constant). Numerical results are presented for the time evolution of such a $q$-bubble with gravity turned off and with gravity turned on. For small enough bubbles and a $q$-field energy scale sufficiently below the gravitational energy scale $E_text{Planck}$, the vacuum energy of the $q$-bubble is found to disperse completely. For large enough bubbles and a finite value of $E_text{Planck}$, the vacuum energy of the $q$-bubble disperses only partially and there occurs gravitational collapse near the bubble center.
Following recent works on corner charges we investigate the boundary structure in the case of the theory of gravity formulated as a constrained BF theory. This allows us not only to introduce the cosmological constant, but also explore the influence of the topological terms present in the action of this theory. Established formulas for charges resemble previously obtained ones, but we show that they are affected by the presence of the cosmological constant and topological terms. As an example we discuss the charges in the case of the AdS--Schwarzschild solution and we find that the charges give correct values.
A universal relation between the leading correction to the entropy and extremality was gotten in the work of Goon and Penco. In this paper, we extend this work to the massive gravity and investigate thermodynamic extremality relations in a topologically higher-dimensional black hole. A rescaled cosmological constant is added to the action of the massive gravity as a perturbative correction. This correction modifies the extremality bound of the black hole and leads to the shifts of the mass, entropy, etc. The Goon-Penco relation is gotten. Regarding the cosmological constant as a variable related to pressure, we get the thermodynamic extremality relations between the mass and pressure, charge, parameters $c_i$ by accurate calculations, respectively. Finally, these relations are verified by a triple product identity, which shows that the universal relation exists in black holes.
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