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Register a new userApproximating tunneling rates in multi-dimensional field spaces
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Quantum mechanics makes the otherwise stable vacua of a theory metastable through the nucleation of bubbles of the new vacuum. This in turn causes a first order phase transition. These cosmological phase transitions may have played an important role in settling our universe into its current vacuum, and they may also happen in future. The most important frameworks where vacuum decay happens contain a large number of fields. Unfortunately, calculating the tunneling rates in these models is very time-consuming. In this paper we present a simple approximation for the tunneling rate by reducing it to a one-field problem which is easy to calculate. We demonstrate the validity of this approximation using our recent code Anybubble for several classes of potentials.
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We show that the Laplace-Beltrami equation $square_6 a =j$ in $(setR^6,eta)$, $eta := mathrm{diag}(+----+)$, leads under very moderate assumptions to both the Maxwell equations and the conformal Eastwood-Singer gauge condition on conformally flat spaces including the spaces with a Robertson-Walker metric. This result is obtained through a geometric formalism which gives, as byproduct, simplified calculations. In particular, we build an atlas for all the conformally flat spaces considered which allows us to fully exploit the Weyl rescalling to Minkowski space.
We construct analytical and regular solutions in four-dimensional General Relativity which represent multi-black hole systems immersed in external gravitational field configurations. The external field background is composed by an infinite multipolar expansion, which allows to regularise the conical singularities of an array of collinear static black holes. A stationary rotating generalisation is achieved by adding independent angular momenta and NUT parameters to each source of the binary configuration. Moreover, a charged extension of the binary black hole system at equilibrium is generated. Finally, we show that the binary Majumdar-Papapetrou solution is consistently recovered in the vanishing external field limit. All of these solutions reach an equilibrium state due to the external gravitational field only, avoiding in this way the presence of any string or strut defect.
The paper has been withdrawn by the author.
We revisit the famous Coleman-de Luccia formalism for decay of false vacuum in gravitational theory. Since the corresponding wave function is time-independent we argue that its instantons interpretation as the decay rate probability is problematic. We instead propose that such phenomenon can better be described by the Wheeler-de Witts wave function. To do so, the Hamilton-Jacobi formalism is employed in the WKB approximation. The scalar and gravitational fields can then be treated as a two-dimensional effective metric. For a particular case of dS-to-dS tunneling, we calculated the wave function and found that it depends only on the potential of the false, and not on the true, vacuum; reminiscent of, though in totally different formalism with, the Hawking-Moss result. In general, this alternative approach might have significant impact on the study of very early universe and quantum cosmology.
Reissner-Nordstrom Anti-de Sitter (RNAdS) black holes are unstable against the charged scalar field perturbations due to the well-known superradiance phenomenon. We present the time domain analysis of charged scalar field perturbations in the RNAdS black hole background in general dimensions. We show that the instabilities of charged scalar field can be explicitly illustrated from the time profiles of evolving scalar field. By using the Prony method to fit the time evolution data, we confirm the mode that dominates the long time behavior of scalar field is in accordance with the quasinormal mode from the frequency domain analysis. The superradiance origin of the instability can also be demonstrated by comparing the real part of the dominant mode with the superradiant condition of charged scalar field. It is shown that all the unstable modes are superradiant, which is consistent with the analytical result in the frequency domain analysis. Furthermore, we also confirm there exists the rapid exponential growing modes in the RNAdS case, which makes the RNAdS black hole a good test ground to investigate the nonlinear evolution of superradiant instability.
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