The main objective of this thesis is to study the behavior of black objects in external fields, for example black holes and black strings in 4 and 5-dimensional spacetimes respectively. In particular, to analyze how external fields affect horizons and the internal structure of such objects, to study their properties, and tocunderstand how the spacetime fabric works. The thesis contains three chapters. In Chapters 1 and 2 we study the interior of 4-dimensional static, axisymmetric, electrically neutral and electrically charged distorted black holes. We analyze how external static and axisymmetric distortions affect the interior of such black holes. In particular, we study the behavior of the interior solution of an electrically neutral black hole near its horizon and singularity. The analysis shows that there exists a certain duality between the event horizon and the singularity. As a special example, we study the interior of a compactified 4-dimensional Schwarzschild black hole. In the case of an electrically charged black hole, a similar duality exists between its event and Cauchy horizons. The duality implies that the Cauchy horizon remains regular, provided the distortion is regular at the event horizon. Extension of the general theory of relativity to higher dimensional spacetimes brings a large variety of black objects whose boundary, the event horizon, may be of a complicated structure. One such object is a black string. In Chapter 3 we discuss the so-called Gregory-Laflamme instability of 5-dimensional black strings in a spacetime with one compact dimension and their topological phase transitions. Here we consider black strings with electric or magnetic charge. Linear static perturbations of these objects indicate the presence of a threshold unstable mode. An analysis of such mode shows that an electrically charged black string is less stable than a neutral one. The situation is opposite for a magnetically charged black string. An analysis of 5-dimensional extremal black string with electric charge shows a continuous spectrum of unstable threshold modes. The results presented in this thesis may have applications in the theory of classical 4-dimensional black holes and in the modern theoretical models of higher dimensions.

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A number of models of nature incorporate dimensions beyond our observed four. In this thesis we examine some examples and consequences of classical instabilities that emerge in the higher-dimensional theories of gravity which can describe their low energy phenomenology. <br /><br /> We first investigate a gravitational instability for black strings carrying momentum along an internal direction. We argue that this implies a new type of solution that is nonuniform along the extra dimension and find that there is a boost dependent critical dimension for which they are stable. Our analysis implies the existence of an analogous instability for the five-dimensional black ring. We construct a simple mode of the black ring to aid in applying these results and argue that such rings should exist in any number of space-time dimensions. <br /><br /> Next we consider a recently constructed class of nonsupersummetric solutions of type IIB supergravity which are everywhere smooth and have no horizon. We demonstrate that these solutions are all classically unstable. The instability is a generic feature of horizonless geometries with an ergoregion. We consider the endpoint of this instability and argue that the solutions decay to supersymmetric configurations. We also comment on the implications of the ergoregion instability for Mathur's 'fuzzball' proposal. <br /><br /> Finally, we consider an interesting braneworld cosmology in the Randall-Sundrum scenario constructed using a bulk space-time which corresponds to a charged AdS black hole. In particular, these solutions appear to 'bounce', making a smooth transition from a contracting to an expanding phase. By considering the space-time geometry more carefully, we demonstrate that generically in these solutions the brane will encounter a singularity in the transition region.

A number of models of nature incorporate dimensions beyond our observed four. In this thesis we examine some examples and consequences of classical instabilities that emerge in the higher-dimensional theories of gravity which can describe their low energy phenomenology. <br /><br /> We first investigate a gravitational instability for black strings carrying momentum along an internal direction. We argue that this implies a new type of solution that is nonuniform along the extra dimension and find that there is a boost dependent critical dimension for which they are stable. Our analysis implies the existence of an analogous instability for the five-dimensional black ring. We construct a simple mode of the black ring to aid in applying these results and argue that such rings should exist in any number of space-time dimensions. <br /><br /> Next we consider a recently constructed class of nonsupersummetric solutions of type IIB supergravity which are everywhere smooth and have no horizon. We demonstrate that these solutions are all classically unstable. The instability is a generic feature of horizonless geometries with an ergoregion. We consider the endpoint of this instability and argue that the solutions decay to supersymmetric configurations. We also comment on the implications of the ergoregion instability for Mathur's 'fuzzball' proposal. <br /><br /> Finally, we consider an interesting braneworld cosmology in the Randall-Sundrum scenario constructed using a bulk space-time which corresponds to a charged AdS black hole. In particular, these solutions appear to 'bounce', making a smooth transition from a contracting to an expanding phase. By considering the space-time geometry more carefully, we demonstrate that generically in these solutions the brane will encounter a singularity in the transition region.