An Explicit Formula for the Matrix Logarithm

We present an explicit polynomial formula for evaluating the principal logarithm of all matrices lying on the line segment $\{I(1-t)+At:t\in [0,1]\}$ joining the identity matrix $I$ (at $t=0$) to any real matrix $A$ (at $t=1$) having no eigenvalues on the closed negative real axis. This extends to the matrix logarithm the well known Putzer's method for evaluating the matrix exponential.Comment: 6 page

The Blackbody Radiation in D-Dimensional Universes

The blackbody radiation is analyzed in universes with $D$ spatial dimensions. With the classical electrodynamics suited to the universe in focus and recurring to the hyperspherical coordinates, it is shown that the spectral energy density as well as the total energy density are sensible to the dimensionality of the universe. Wien's displacement law and the Stefan-Boltzmann law are properly generalized

Visco-elastic regularization and strain softening

In this paper it is intended to verify the capacity of regularization of the numerical solution of an elasto-plastic problem with linear strain softening. The finite element method with a displacement approach is used. Drucker-Prager yield criteria is considered. The radial return method is used for the integration of the elasto-plastic constitutive relations. An elastovisco- plastic scheme is used to regularize the numerical solution. Two constitutive laws have been developed and implemented in a FE-program, the first represent the radial return method applied to Drucker-Prager yield criteria and the second is a time integration procedure for the Maxwell visco-elastic model. Attention is paid to finite deformations. An associative plastic flow is considered in the Drucker-Prager elasto-plastic model. The algorithms are tested in two problems with softening. Figures showing the capability of the algorithms to regularize the solution are presented

Stability of naked singularities and algebraically special modes

We show that algebraically special modes lead to the instability of naked singularity spacetimes with negative mass. Four-dimensional negative-mass Schwarzschild and Schwarzschild-de Sitter spacetimes are unstable. Stability of the Schwarzschild-anti-de Sitter spacetime depends on boundary conditions. We briefly discuss the generalization of these results to charged and rotating singularities.Comment: 6 pages. ReVTeX4. v2: Minor improvements and extended discussion on boundary conditions. Version to appear in Phys. Rev.

Characterization of echoes: A Dyson-series representation of individual pulses

The ability to detect and scrutinize gravitational waves from the merger and coalescence of compact binaries opens up the possibility to perform tests of fundamental physics. One such test concerns the dark, nature of compact objects: are they really black holes? It was recently pointed out that the absence of horizons -- while keeping the external geometry very close to that of General Relativity -- would manifest itself in a series of echoes in gravitational wave signals. The observation of echoes by LIGO/Virgo or upcoming facilities would likely inform us on quantum gravity effects or unseen types of matter. Detection of such signals is in principle feasible with relatively simple tools, but would benefit enormously from accurate templates. Here we analytically individualize each echo waveform and show that it can be written as a Dyson series, for arbitrary effective potential and boundary conditions. We further apply the formalism to explicitly determine the echoes of a simple toy model: the Dirac delta potential. Our results allow to read off a few known features of echoes and may find application in the modelling for data analysis.Comment: 12 pages, 3 figures. v2: Minor updates, including revised notation for permutations and further elaboration on the concluding remarks. Version to appear in Physical Review