Regular bulk solutions and black strings from dynamical braneworlds with variable tension

Regular black strings solutions associated to a dynamical Friedmann-Robertson-Walker braneworld are obtained as a particular case of a bulk metric in the context of a variable tension braneworld. By analyzing the 5D Kretschmann invariants, we show that the variable brane tension is capable of attenuating the bulk physical singularities along some eras of the evolution of the Universe. nIn particular, the black string is analyzed for the McVittie metric on an Eötvös fluid braneworld, wherein the fluid dynamical brane tension depends on the brane temperature. The whole bulk is shown to be regular for a universe dominated by nonrelativistic matter or by relativistic matter/radiation, as the cosmological time elapses. In a particular case, the black strings are shown to have finite extension along the extra dimension, which prominently modify the higher-dimensional soft physical singularities. For a universe dominated by matter or radiation, we show that the bulk is regular as the cosmological time elapses, as an effect of the variable brane tension.

Figure 1

Graphic of the black string warped horizon $g_{\theta \theta }(t,\mathrm{r},y)$, with terms due to the variable brane tension, along $y$, as function of the time $t$. Here $a(t)=\exp (H_{0}t)$.

Figure 2

Graphic of the black string warped horizon $g_{\theta \theta }(t,\mathrm{r},y)$, with extra terms due to the variable brane tension along $y$, as function of the time $t$. Here $a(t)\propto t^{\beta /2}$.

Figure 3

Graphic of the black string for a universe dominated by relativistic matter or radiation, where $a(t)\propto \exp (H_{0}t)$.

Figure 4

Graphic of the black string for a universe dominated by relativistic matter or radiation, where $a(t)\propto t^{\beta /2}$.

Figure 5

Plot of the 5D Kretschmann scalar ${}^{(5)}\xi$ as a function of time and $\mathfrak{r}$, for the scale factor $a(t)\propto \exp (H_{0}t)$.

Figure 6

Plot of the 5D Kretschmann scalar ${}^{(5)}\xi$ as a function of time and $\mathfrak{r}$, for the scale factor $a(t)\propto t^{\beta /2}$.