If you don’t know who the Kardashians are, well, check this page. For some, Kardashian stands for being famous without really anybody knowing why you are famous.
Neil Hall devised a Kardashian index for scientists who are popular on social media (and probably weigh in more on public debates) rather than because of their citations in peer reviewed scientific journals. One came become more popular because you gave a TED-talk, but that won’t get you cited more often.
It’s a different take on the matter than the question if Google isn’t a better kind of metric than scientific citations.
Do bear in mind, Hall notes:
“I don’t blame Kim Kardashian or her science equivalents for exploiting their fame, who wouldn’t? However, I think it’s time that we develop a metric that will clearly indicate if a scientist has an overblown public profile so that we can adjust our expectations of them accordingly.”

I for myself think the problem lies with scientists who are being cited often, but who stay away from public debate (be it on social media, be it anywhere else).
Abstract of the paper:
In the era of social media there are now many different ways that a scientist can build their public profile; the publication of high-quality scientific papers being just one. While social media is a valuable tool for outreach and the sharing of ideas, there is a danger that this form of communication is gaining too high a value and that we are losing sight of key metrics of scientific value, such as citation indices. To help quantify this, I propose the ‘Kardashian Index’, a measure of discrepancy between a scientist’s social media profile and publication record based on the direct comparison of numbers of citations and Twitter followers.