The concept of rejuvenating planets around dead stars is highly speculative and unsupported by concrete scientific evidence. When a star dies, it undergoes significant changes, including a dramatic loss of its outer layers and a reduction in its luminosity. These changes make it unlikely for a planet to maintain a stable orbit or sustain conditions necessary for life.

Dead stars are usually either white dwarfs, neutron stars, or black holes. White dwarfs are the remnants of stars that have shed their outer layers and collapsed under the force of their own gravity. They are extremely dense and have a very low surface temperature. Neutron stars are the collapsed cores of massive stars that have undergone a supernova explosion. They are even denser than white dwarfs and have an extremely strong magnetic field. Black holes are the result of the gravitational collapse of massive stars that have reached the end of their lifespan. They have an intense gravitational pull and are theorized to be regions where space and time are distorted.

In all these cases, the environment around a dead star is vastly different from that around a living star. The lack of sustained energy output and the extreme conditions (such as intense magnetic fields or gravitational forces) would make it challenging for a planet to survive, let alone rejuvenate.

However, it's important to note that the field of astrobiology is constantly evolving, and new discoveries and theories may shed light on this concept in the future. Ongoing research and technological advancements may provide more insight into the possibilities and limitations of life around dead stars.